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A space is said to be KC – space if compact subsets are closed. A KC space (X,τ) is said to be Katetov – KC if there is a minimal KC – topology σ ⊆ τ. is every sequential KC - space Katetov - KC? I know that every KC space is not Katetov - KC. do you have any example to show it?

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    $\begingroup$ I wish there would be less of a tongue twister (mind twister)? $\endgroup$
    – Włodzimierz Holsztyński
    Commented Aug 24, 2013 at 3:00

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It was shown in "The FDS-property and spaces in which compact sets are closed" (2004) by Alas, Tkachenko, Tkachuk and Wilson that every sequential KC-space is Katetov-KC (see Corollary 2.6).

The fact that not every KC-space is Katetov-KC was shown by Fleissner in "A $T_B$-space which is not Katetov $T_B$" (1980).

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  • $\begingroup$ I read the whole article but I did not understand which part was exactly ma answer. $\endgroup$
    – Alireza
    Commented Aug 6, 2013 at 18:40

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